When dealing with basic Fourier–Bessel expansions, due to convergence issues, it is crucial to know the asymptotic behavior of the third Jackson \(q\) -Bessel function when computed in its own shifted zeros. For this purpose, in the sequel of Rahman, as pointed out by Koelink and Swarttouw [1]}, “the intermingling of (ordinary) analysis and \(q\) -analysis may be fruitful”.
